Rectangular wave impulse generator



March 29, 1949. VARELA 2,465,407

RECTANGULAR WAVE IMPULSE GENERATOR Filed March so, 1945 2 She'ets-Sheet1 f "iffl I [A A5! LSINSQJT l 4 sllvzwr 1 i 1* '1 I :ElE-z-4.

a t V l ARTHUR A. VARELA March 29, 1949. \(ARELA 2,465,407

RECTANGULAR wAvE IMPULSE GENERATOR Filed March 30, 1943 2 Sheets-Sheet 2ARTHUR A.VARELA A W W Patented Mar. 29, 1949 RECTANGULAR WAVE IMPULSEGENERATOR Arthur A. Varela, Washington, D. 0.

Application March 30, 1943,

15 Claims.

(Granted under Serial No 481,108

the act of March 3, 1883, as

amended April 30, 1928; 370 O. G. 757) This invention is directed to theproblem of generating rectangular wave electrical impulses, and isparticularly related to systems for accomplishing this object whereinstored energy is periodically discharged through a circuit whichincludes a pulse-shaping filter.

Systems of this type are described in my copending application, S. N.447,671, filed June 19, 1942, wherein a potential storing capacity isperiodically connected to a discharge circuit including anti-resonantcomponents tuned to the fundamentalperiod of the discharge pulse and toits submultiples. I I

According to the invention ofsaid disclosure, a substantially constantcurrent is maintained through the load during a predetermined timeperiod, after which it falls abruptly to zero, thus developing arectangular voltage wave across the load impedance. The constant currentis obtained by the transient response of the anti-resonant filtersections, which are separately tuned to the various alternatincomponents of the applied voltage as determined by Fourier analysis.Under transient application of a resonating voltage to an anti-resonantcircuit the reactive currents in the two branches are not equal and ofinverse phase. as they are in steady state conditions, but diifer by anexponentially decreasing term constituting the inductive transient. Thistransient, being the unbalance'between the inductive and capacitativecurrents, represents the line current for the particular frequencycomponent considered, and the sum of the transients form the total linecurrent. By suitably designing the inductances of the filter, the rateof decay of the transients can be made small enough to generate asubstantially constant current during the period of pulse duration,-which is relatively short.

It is a further characteristic of the system disclosed in theaforementioned application that the voltage across the storing capacitordecreases linearly with the rectangular wave across the load impedance.Since the voltage applied to the filter as a whole is the differencebetween the constant load impedance drop and the storage capacitorvoltage, it is also of saw-tooth form.-

By Fourier analysis it can be shown that the saw-tooth voltages compriseharmonically related alternating components whose amplitudes decrease inproportion to the harmonic number. Consequently, particularly in highvoltage systems, the design requirements for the low harmonic sectionsare very stringent, and the fundamental section is of especiallydifficult, expensive, and heavy construction.

Accordingly, it is the chief object of the invention to eliminate one ofsaid filter sections, preferably the fundamental section, Whilepreservin the function of such section in a generating system of thetype described.

It is another object of this invention to provide a rectangular waveimpulse generating circuit of the type described wherein a filtersection is eliminated, and in which the energy storing circuit itselfconstitutes a circuit component antiresonant at the frequency of theeliminated section.

A further object of the invention is to provide a rectangular waveimpulse generating circuit of particularly economical design for highvoltage operation. I

The invention will be further described with reference to the exemplaryembodiments thereof shown in the drawings, in which:

Fig. 1 is a diagrammatic showing of a simplified rectangular waveimpulse generator embodying the principles of the present invention;

Fig. 2 is a schematic representation of voltage and current componentsof a filter section of the system;

Fig. 3 is a schematic representation of the sawtooth voltage waveresulting from the constant current discharge of the storing circuit,and its direct and alternating voltage components of lower frequency;

Fig. 4 is a schematic representation of the rectangular wave voltageimpulse produced by a generating system of the present invention;

Fig. 5 is a diagrammatic showing of another. rectangular wave impulsegenerator of the present invention, and

Fig. 6 is a diagrammatic rectangular wave present invention.

As shown in Fig. 1, the pulse generating system receives energy from adirect current supply illustrated as battery 5 which may be connected tothe generating system by switch 2. The energy storing circuit 3 may beconnected by switch 41 to the discharge circuit including filter F andload impedance R. The storing circuit comprises capacitors Ca and Cb,and inductance L. For pulse generation, the storage circuit is connectedto the supply to charge the capacitors, and after disconnection from thesupply, is connected to the discharge circuit by switch 4.

The pulse shaping filter F comprises a group of anti-resonant circuitsconnected in series. These filter sections are individually tuned tofrequencies which are harmonically related to a fundamental frequencywhose period is the discharge time of the generator. Consequently theperiods of the filter sections are submultiples of the period of pulseduration. In the circuit as shown. C2-Le constitute a section resonantat the second harmonic, C3L3 at the third harmonic, and in general Cn-Lnis resonant at the nth harmonic. In practice only a limited number orsections need showing of a further impulse generator of the be used, asthe amplitudes of the higher harmonic voltages present in the circuitdecrease in proportion to the harmonic number.

On initiation of the discharge by closing switch 4, the current flowsfrom the storing circuit through filter F and the load impedance R. Thedischarge current is determined by the internal impedance of the storingcircuit, the impedance of the filter circuit, and the load impedance.

In Fig. 1, the storing circuit comprising capacitors Ca and Cb connectedby inductance L is characterized by having an internal impedanceanti-resonant at the fundamental frequency, or at one of the harmonicfrequencies thereof, the corresponding filter section being absent. Forthe reasons outlined above, the storing circuit of Fig. 1 isanti-resonant at the fundamental frequency, and the filter sectionsaccordingly are tuned to the second and higher harmonics thereof.

Considering the energizing voltage of the storing capacitors as er, thevoltage developed across the filter and the internal impedance of thestoring circuit together as es, we have, where E is the originalpotential of the capacitors:

0 id: cJot Where i is the discharge current at any time t.

The voltage set up across the load impedance 62=Ri The voltage asdeveloped by 2' across the filter and the internal impedance of thestoring circuit If we take 63 as above determined as fit), the functionmay be resolved into a constant voltage and alternating voltagecomponents of a series of harmonically related frequencies, by Fourieranalysis. The period of the fundamental component is determined by thedischarge time of the circuit, and the other components are of periodsequal to the sub-multiples of the discharge time.

The current flow may now be determined for each alternating voltagecomponent. The filter sections and the storing circuit are adjusted forparallel resonance to the several voltages. The impedance ofiered eachcomponent by the circuit element resonant thereto is far greater thanthe impedance of the other elements, and consequently the current flowfor the component in the circuit as a whole is substantially determinedby the impedance of its respective element.

The reactive current passed by a parallel resonant circuit underapplication of an alternating voltage of the resonant frequency is, inthe steady state condition, zero. This is due to the phase oppositionand consequent cancellation of the leading current drawn by thecapacitor and the lagging current drawn by the inductor. The linecurrent is negligible due to the high resistance at resonance.

If, however, the alternating voltage is suddenly applied, cancellationdoes not take place, because the current drawn by the inductor differsfrom that drawn in the steady state condition by a transient termexponentially decreasing with time at a rate determined by the ratio R/Lof the coil, whereas the current drawn by the condenser is the same asthat drawn in the steady state condition. The currents in the inductiveand capacitative branches with the applied voltage e and the linecurrent i, are shown in Fig. 2.

Under these transient conditions, the line current, being the differencebetween the currents in the two branches, is manifestly equal to thetransient term of the inductive current, as also shown in Fig. 2.

This is the case for each alternating component of the applied voltage,and therefore the discharge current attributable to the alternatingvoltage components is the sum of the transient terms for eachalternating component as applied to its resonant filter section. In aproperly constructed coil the ratio R/L will be suificiently low topermit consideration of the transient terms as constant currents duringthe period of pulse duration. In addition, the constant or D. C.component of the applied voltage will also cause a substantiallyconstant current in the discharge circuit. The deviations of the D. C.current component and the transients from the desired values are inopposite directions and therefore to a considerable extent cancel.Consequently, during the period of the pulse a substantially constantline current is drawn from the storing capacity.

Determination of this fact shows, further, that the voltage e1 acrossthe storing capacity decreases linearly with time, and that the voltagee2 developed across the load impedance is constant during the pulseduration.

The voltage wave form of e1 is resolvable by Fourier analysis into aconstant term and alternating components as follows:

f (z) =A+A sin we? sin 2am? sin mat Consequently the alternating voltagecomponents supplied to the filter have an amplitude inverselyproportional to their harmonic numbers. The voltage supplied by thestoring capacity, together with the direct and lower harmonicalternating voltage components thereof, are illustrated in Fig. 3. InFig. 4 is shown the square voltage wave developed over the loadimpedance by the constant current i.

In the circuit of Fig. 1 the impedance of the filter may be representedby Z. If a pi section as shown is discharged with a constant current ithrough an impedance Z and a load resistor R, the voltage relations onthe circuit are as follows, using operational notation and infiniteseries:

Since it is desired that the filter impedance Z be a harmonic series ofparallel L-C circuits, with the omission of the fundamental, IZ.1 may beexpressed as follows:

If this value is substituted in the above equation and like frequencyterms are equated, the following relationships are obtained For completedissipation of stored energy in the time interval t=21r/w Where anonlinear load is employed, however, the matching is not critical.

It is often desirable to employ a plurality of storin sections to supplythe energy for pulse generation. The storage sections may be charged inparallel and discharged in series as a Marx generator to produce a highvoltage output. The embodiment of the invention shown in Fig. employs aMarx type voltage multiplier including as storing components pi sectionsof special design.

In Fig. 5 the power supply comprises a halfwave rectifying systemincluding transformer 20 and rectifier 2|. The Marx generator includessimilar pi sections 5, t, l and 8, each comprising an inductance 9, andtwo capacitors l6 and H.

The successive pi sections are connected by chokes I2. The storingcomponents are charged in parallel on the positive half-cycles fedthrough rectifier 2|. and are discharged in series during negative halfcycles by synchronously driven gaps l3. For operating the gaps iii asynchronous motor l4 may advantageously be employed, and energized bythe same A. C. supply as transformer 20.

By operation of gaps 13 the potentials across the successive pi sectionsare connected in series through the filter it to load 22, which, asshown, is a high frequency triode oscillator. During discharge of thestorage circuits a blocking effect is obtained by chokes l2 having atime constant suitable to prevent the discharge of the sections exceptin the desired series relationship.

The filter l5 comprisin parallel tuned components operates inconjunction with the storage circuit to provide a rectangular waveimpulse for operation of the load exactly as in the system of Fig. 1.The discharge circuit includes in series circuit element groups whichare anti-resonant to the fundamental discharge frequency and itsharmonics, the groups referred to being the filter sections and thestoring sections. In the embodirnent of Fig. 5 the storing sections areall tuned to the same irequency which in this case, for the reasonsmentioned, is fundamental frequency, and the corresponding filtersection is absent. Suitable values for the capacitors and inductancesmay be calculated by the formulas given below in connection with Fig. 6.

- The inductance i5 is placed in the discharge circuit to avoid thenecessity for a multiplicity of filter sections, and functions to limitvariations in the discharge current that would otherwise be caused byhigh frequency components.

The system disclosed in Fig. '6 includes a halfwave rectifier supplycomprising power trans former 2i) and rectifier 2i ieedii energy storingpi sections 23, 24, and 25 connected for parallel charging by chokes Onthe positive haliwaves the capacitors lil ll of each pi section arecharged through rectifier 3.1 with increasing potentials which areapplied across snarl: discharge gaps 25. These gaps are adjusted tobreakdown preferably slightly below the peak voltage to insuredependable operation. On discharge of the gaps 26, a high potentialrectangular wave impulseis applied to load impedance R. through filter21, in the manner described above in connection with the system shown inFig. 1.

As indicated in Fig. 6, the storage circuit may consist of any desirednumber of storage sections, and the filter 2'! may also be provided withany desired number of parallel resonant sections.

If the number of storing sections is represented by N, and the number offilter sections is it, then if the value of capacitors It is indicatedCb and H by Ca, and inductance 9 by L, then If the value of the filtercondenser components 23 are represented by C2, C3 and Cu, and theinductances 32, 33, 34 etc. are represented by L2, L3 and Ln, where n isthe harmonic number of the section:

For complete dissipation of in time t the load resistance is followingrelation:

It will therefore be seen that if it is desired to employ a plurality ofstoring sections instead of the single section generator system shown inFig. 1, the storage capacitors are multiplied in proportion to thenumber of sections used and the inductance, expressed above as inverselyproportional to the capacity, is therefore divided by the number ofsections employed, so that the resonant frequency of the storagesections will remain the same. The filter sections will be the same inboth cases.

The invention described herein may be ll1&l1.lfactured and used by orfor the Government of the United States of America for governmentalpurposes without the payment of any royalties thereon or therefor.

I claim:

1. In a rectangular wave impulse generating system, an energy storincircuit and a discharge circuit including pulse shaping filter means,said energy storing circuit comprising a pi section anti-resonant at afrequency of a period equal to the impulse duration time or asub-multiple thereof.

2. A flat topped wave generating system comprising a plurality ofcircuit sections antiresonant at frequencies ofperiods equal to theimpulse duration time and its submultiples, one of said anti-resonantsections including storing capacitor means, and switch means in saidsystem operative to discharge said storing capacitor means through thesystem to generate the impulse.

3. In a rectangular wave impulse generating system, an energy storingcircuit comprising a pi section, and a discharge circuit including aplurality of filter sections and a load impedance, said filter sectionand load impedance being connectable in series across the pi section,said pi section and filter sections being. anti-resonant at frequenciesof periods equal to the impulse duration time and its submultiples.

4. In a rectangular wave impulse generating system, an energy storingcircuit comprising a pi section anti-resonant at a fundamental frequencythe stored energy determined by the of a period equal to the impulseduration time, and a filter circuit including a plurality of sec tionsanti-resonant at harmonics of said fundamental frequency, said sectionsbeing connectable in series with each other across the pi section.

5. In a rectangular wave impulse generating system, an energy storingcircuit comprising a plurality of pi sections, and a discharge circuitincluding a plurality of filter sections connectable across the pisection in series with each other, said circuit sections beinganti-resonant at frequencies of periods equal to the impulse durationtime and its submultiples.

6. In a rectangular Wave impulse generating system, an energy storingcircuit comprising a plurality of identical sections, and a dischargecircuit including a plurality of filter sections connectable across thepi section in series with each other, said circuit sections beinganti-resonant at frequencies of periods equal to the impulse durationtime and its submultiples.

7. In a rectangular Wave impulse generating system, an energy storingcircuit comprising a plurality of identical pi sections, and a dischargecircuit including a plurality of filter sections connectable across thepi section in series with each other, said circuit sections beinganti-resonant at frequencies of periods equal to the impulse durationtime and its submultiples.

8. In a rectangular wave impulse generating system, an energy storingcircuit comprising a plurality of pi sections anti-resonant at afundamental frequency of a period equal to the impulse duration time,and a discharge circuit including filter sections connectable across thepi section in series with each other anti-resonant at frequenciesharmonically related to said fundamental frequency connectable acrossthe pi section in series with each other.

9. In a rectangular wave impulse generating system, an energy storingcircuit anti-resonant at a fundamental frequency of a period equal tothe impulse duration time, and a discharge circuit includingpulse-shaping filter sections connectable across the pi section inseries with each other anti-resonant at frequencies harmonically relatedto said fundamental frequency connectable across the pi section inseries with each other.

10. A rectangular wave impulse generating sys tem including energystoring circuit means and a discharge circuit therefor comprising filtercircuit means having a series of inductance-capacity circuitsconnectable across the storing circuit in series with each other, thecapacitors of the filter circuit means all having the same value, andthe energy storing circuit means including a low pass pi section, thecapacitor in series with the inductance having a value of 4/3 of one ofthe filter capacitors, and the other capacitor having a value equal to2/3 of one of the filter capacitors.

11. A rectangular wave impulse generating system including energystoring circuit means and a discharge circuit therefor comprising filtercircuit means having a series of inductance-capacity circuitsconnectable across the storing circuit in series with each other, thecapacitors of the filter circuit means all having the same value, andthe energy storing circuit means including a low pass pi section, thecapacitor in series with the inductance having a value of 4/3 of one ofthe filter capacitors, and the other capacitor having a value equal to2/3 of one of the filter capacitors, the

low pass pi section being anti-resonant at a fundamental frequency of aperiod equal to the impulse duration time, and the inductance-capacityfilter circuits being anti-resonant at frequencies harmonically relatedto said fundamental frequency.

12. A rectangular wave impulse generating system including energystoring circuit means comprising a plurality N of low pass pi sectionsand a discharge circuit therefor comprising filter circuit means havinga series of inductance-capacity circuits connectable across the storingcircuit in series with each other, the capacitors of the filter circuitmeans all having the same value, the capacitors of the low pass pisection in series with the inductance having a value of 4N/3 of one ofthe filter capacitors, and the other capacitors of the low pass pisections having a value of 2N/3 of one of the filter capacitors.

13. A rectangular wave impulse generating system including energystoring circuit means comprising a plurality N of low pass pi sectionsand a discharge circuit therefor comprising filter circuit means havinga series of inductance-capacity circuits connectable across the storingcircuit in series with each other, the capacitors of the filter circuitmeans all having the same value, the capacitors of the low pass pisection in series with the inductance having a value of 4N/3 of one ofthe filter capacitors, and the other capacitors of the low pass pisections having a value of 2N/3 of one of the filter capacitors, the lowpass pi sections being all anti-resonant at a fundamental frequency of aperiod equal to the impulse duration time, and the inductance-capacityfilter circuits being anti-resonant at frequencies harmonically relatedto said fundamental frequency.

14. In a wave impulse generator, an energy storing circuit, a dischargecircuit including a pulse shaping network and a load impedance, saidenergy storing circuit comprising inductance and capacity means. meansfor charging the capacity means to a predetermined voltage, and meansfor connecting the storage circuit to the discharge circuit to dischargethe storage circuit and generate an impulse, the energy storage circuitbeing anti-resonant at a frequency of a period equal to the impulseduration or a submultiple thereof.

15. In a wave impulse generator, an energy storing circuit, a dischargecircuit including a pulse shaping network and a load impedance. saidenergy storing circuit comprising inductance and capacity means, meansfor charging the capacity means to a predetermined voltage, and meansfor connecting the storage circuit to the discharge circuit to dischargethe storage circuit and generate an impulse, the energy storage circuitand the pulse shaping network being anti-resonant at frequencies ofperiods equal to the impulse duration and its sub-multiples.

ARTHUR A. VARELA.

REFERENCES CITED The following references are of record in the file ofthis patent:

UNITED STATES PATENTS

